LCM of 68 and 216
3672 is the LCM of 68 and 216. The step-by-step solution using prime factors and special division methods is one of the simple methods to easily understand how to find what is the LCM of 68 and 216, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 68 and 216?
lcm (68 216) = (?)
68 => 2 x 2 x 17
216 => 2 x 2 x 2 x 3 x 3 x 3
= 2 x 2 x 17 x 2 x 3 x 3 x 3
= 3672
lcm (68 and 216) = 3672
3672 is the LCM of 68 and 216.
where,
68 is a positive integer,
216 is a positive integer,
3672 is the LCM of 68 and 216,
{2 x 2} in {2 x 2 x 17, 2 x 2 x 2 x 3 x 3 x 3} are the common factors of 68 and 216,
{17 x 2 x 3 x 3 x 3} in {2 x 2 x 17, 2 x 2 x 2 x 3 x 3 x 3} are the uncommon factors of 68 and 216.
Use in Mathematics: LCM of 68 and 216
The below are some of the mathematical applications where lcm of 68 and 216 can be used:
- to find the least number which is exactly divisible by 68 and 216.
- to find the common denominator for two fractions having 68 and 216 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 68 and 216 helps to find the exact time when two similar and recurring events with different time schedule happens together at the same time. For example, the real world problems involve lcm in situations to find at what time the bells A and B all toll together, if bell A tolls at 68 seconds and bell B tolls at 216 seconds repeatedly. The answer is that all bells A and B toll together at 3672 seconds for the first time, at 7344 seconds for the second time, at 11016 seconds for the third time and so on.
Important Notes: 68 and 216 lcm
The below are the important notes to be remembered while solving the lcm of 68 and 216:
- The common prime factors and the remaining prime factors of 68 and 216 should be multiplied to find the least common multiple of 68 and 216, when solving lcm by using prime factors method.
- The results of lcm of 68 and 216, and the lcm of 216 and 68 are identical, it means the order of given numbers in the lcm calculation doesn't affect the results.
How-to: What is the LCM of 68 and 216?
The below solved example with step by step work shows how to find what is the lcm of 68 and 216 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 68 and 216?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 68
B = 216
What to be found:
find the lcm of 68 and 216
step 2 Find the prime factors of 68 and 216:
Prime factors of 68 = 2 x 2 x 17
Prime factors of 216 = 2 x 2 x 2 x 3 x 3 x 3
step 3 Identify the repeated and non-repeated prime factors of 68 and 216:
{2, 2} are the most repeated factors and {17 x 2 x 3 x 3 x 3} are the non-repeated factors of 68 and 216.
step 4 Find the product of repeated and non-repeated prime factors of 68 and 216:
= 2 x 2 x 17 x 2 x 3 x 3 x 3
= 3672
lcm(68 and 216) = 3672
Hence,
lcm of 68 and 216 is 3672
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 68 and 216.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 68 and 216
What to be found:
lcm (68, 216) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
68 and 216
step 3 Choose the divisor which divides each or most of the given integers (68 and 216), divide each integers separately and write down the quotient in the next line right under the respective integers. Bring down the integer to the next line if any integer in 68 and 216 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 68 | 216 |
| 2 | 34 | 108 |
| 2 | 17 | 54 |
| 3 | 17 | 27 |
| 3 | 17 | 9 |
| 3 | 17 | 3 |
| 17 | 17 | 1 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 68 and 216:
= 2 x 2 x 2 x 3 x 3 x 3 x 17
= 3672
LCM(68, 216) = 3672
The LCM of two numbers 68 and 216 is 3672